TSTP Solution File: SEU096+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:57:00 EDT 2023
% Result : Theorem 4.58s 2.13s
% Output : Refutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 85
% Syntax : Number of formulae : 147 ( 15 unt; 25 typ; 0 def)
% Number of atoms : 400 ( 6 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 822 ( 40 ~; 2 |; 209 &; 504 @)
% ( 1 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 3 con; 0-2 aty)
% Number of variables : 155 ( 0 ^; 103 !; 52 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(relation_inverse_image_type,type,
relation_inverse_image: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(natural_type,type,
natural: $i > $o ).
thf(being_limit_ordinal_type,type,
being_limit_ordinal: $i > $o ).
thf(positive_rationals_type,type,
positive_rationals: $i ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(transfinite_sequence_type,type,
transfinite_sequence: $i > $o ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(relation_image_type,type,
relation_image: $i > $i > $i ).
thf(function_yielding_type,type,
function_yielding: $i > $o ).
thf(relation_non_empty_type,type,
relation_non_empty: $i > $o ).
thf(with_non_empty_elements_type,type,
with_non_empty_elements: $i > $o ).
thf(ordinal_yielding_type,type,
ordinal_yielding: $i > $o ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,axiom,
? [A: $i] :
( ( element @ A @ positive_rationals )
& ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_arytm_3) ).
thf(153,plain,
? [A: $i] :
( ( element @ A @ positive_rationals )
& ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
thf(93,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(74,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(118,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(45,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(209,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(34,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(175,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(115,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
? [A: $i] :
( ( element @ A @ positive_rationals )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_arytm_3) ).
thf(120,plain,
? [A: $i] :
( ( element @ A @ positive_rationals )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(55,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A )
& ( ordinal_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal2) ).
thf(247,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A )
& ( ordinal_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(31,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(164,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(9,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(84,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(233,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(43,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(201,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(46,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(220,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(57,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(260,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(70,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(252,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(42,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(197,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(224,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(17,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
thf(109,plain,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(237,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(54,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(244,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(44,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( function_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funcop_1) ).
thf(205,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( function_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(59,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(264,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(36,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(180,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(28,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(149,plain,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(26,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(144,plain,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ordinal @ A ) )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_arytm_3) ).
thf(159,plain,
! [A: $i] :
( ( ( empty @ A )
& ( ordinal @ A ) )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(187,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(18,axiom,
~ ( empty @ positive_rationals ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
thf(113,plain,
~ ( empty @ positive_rationals ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(177,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(127,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) )
=> ( with_non_empty_elements @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_funct_1) ).
thf(231,plain,
! [A: $i] :
( ( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) )
=> ( with_non_empty_elements @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(14,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( being_limit_ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
thf(99,plain,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( being_limit_ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(87,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(104,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_ordinal1) ).
thf(171,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(25,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(139,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(146,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(190,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(37,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(183,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(168,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(58,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(262,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(107,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(24,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(136,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(60,axiom,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(268,plain,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(79,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(195,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(23,axiom,
! [A: $i] :
( ( element @ A @ positive_rationals )
=> ( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_arytm_3) ).
thf(131,plain,
! [A: $i] :
( ( element @ A @ positive_rationals )
=> ( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A )
& ( natural @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( subset @ A @ ( relation_rng @ B ) )
& ( finite @ ( relation_inverse_image @ B @ A ) ) )
=> ( finite @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( subset @ A @ ( relation_rng @ B ) )
& ( finite @ ( relation_inverse_image @ B @ A ) ) )
=> ( finite @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(62,plain,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( subset @ A @ ( relation_rng @ B ) )
& ( finite @ ( relation_inverse_image @ B @ A ) ) )
=> ( finite @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(61,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(277,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(90,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(49,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(227,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(47,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(222,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(280,plain,
$false,
inference(e,[status(thm)],[88,153,93,74,118,209,175,82,115,120,247,164,84,233,201,220,260,70,252,197,224,109,193,237,244,205,264,180,149,144,159,187,113,76,177,127,231,99,87,104,171,139,146,190,183,168,262,107,242,136,268,79,195,131,68,62,277,90,227,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 13:08:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/0.99 % [INFO] Parsing done (136ms).
% 1.28/1.00 % [INFO] Running in sequential loop mode.
% 1.86/1.25 % [INFO] eprover registered as external prover.
% 1.86/1.25 % [INFO] cvc4 registered as external prover.
% 1.95/1.26 % [INFO] Scanning for conjecture ...
% 2.11/1.34 % [INFO] Found a conjecture and 59 axioms. Running axiom selection ...
% 2.24/1.40 % [INFO] Axiom selection finished. Selected 59 axioms (removed 0 axioms).
% 2.50/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.50/1.46 % [INFO] Type checking passed.
% 2.59/1.47 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.58/2.13 % External prover 'e' found a proof!
% 4.58/2.13 % [INFO] Killing All external provers ...
% 4.58/2.13 % Time passed: 1615ms (effective reasoning time: 1126ms)
% 4.58/2.13 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.58/2.13 % Axioms used in derivation (59): cc1_arytm_3, rc4_funct_1, fc8_arytm_3, rc2_relat_1, fc6_relat_1, fc2_ordinal1, antisymmetry_r2_hidden, cc2_finset_1, t147_funct_1, fc1_xboole_0, cc2_arytm_3, fc4_relat_1, t1_subset, rc4_ordinal1, rc3_funct_1, rc3_arytm_3, cc1_relat_1, fc6_funct_1, rc1_funct_1, rc3_relat_1, t6_boole, cc4_arytm_3, rc2_subset_1, cc2_ordinal1, t5_subset, rc1_funcop_1, t4_subset, rc1_arytm_3, rc2_arytm_3, cc1_ordinal1, rc5_funct_1, t7_boole, cc1_funct_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, cc3_ordinal1, rc3_ordinal1, rc2_ordinal2, cc2_funct_1, t17_finset_1, t3_subset, existence_m1_subset_1, rc1_ordinal1, rc1_relat_1, rc2_finset_1, reflexivity_r1_tarski, rc2_ordinal1, rc3_finset_1, rc1_ordinal2, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, t2_subset, fc12_relat_1, fc8_relat_1, fc13_finset_1, rc2_xboole_0
% 4.58/2.13 % No. of inferences in proof: 122
% 4.58/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1615 ms resp. 1126 ms w/o parsing
% 4.80/2.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.80/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------